Bounds on a regression coefficient under omitted-variable bias

Computes the identified set for the coefficient on the primary independent variable in the infeasible long regression, across a grid of sensitivity parameters. Implements the analyses of Diegert, Masten & Poirier (2026) (the default) and of Oster (2019) extended by Masten & Poirier (2026).

Usage

regsen_bounds(
  formula,
  data,
  analysis = c("dmp", "oster"),
  compare = NULL,
  nocompare = NULL,
  rxbar = NULL,
  rybar = Inf,
  cbar = 1,
  rybar_expr = NULL,
  delta = NULL,
  r2long = 1,
  maxovb = NA,
  delta_type = c("eq", "bound"),
  r2long_type = c("eq", "relative"),
  maxovb_type = c("bound", "relative"),
  beta = "sign",
  product = TRUE,
  ngrid = 200L,
  subset = NULL
)

Arguments

formula: Two-sided formula: y ~ x + w1 + w2 + .... The first right-hand-side variable is the primary independent variable; the rest are controls.
data: A data.frame.
analysis: Which sensitivity analysis to run: "dmp" (default) or "oster".
compare: Optional character vector of variables to use as the comparison set. Defaults to all controls if neither compare nor nocompare is given.
nocompare: Optional character vector of controls to exclude from the comparison set.
rxbar, rybar, cbar: (DMP) Numeric vectors of sensitivity-parameter values to sweep over. rybar = Inf (the default) gives the no-rybar case; setting it finite invokes the global-optimization code path.
rybar_expr: (DMP) A function function(rxbar) rybar to set rybar as a function of rxbar (the only supported form in the Stata source is rybar = rxbar, i.e. function(rxbar) rxbar).
delta, r2long, maxovb: (Oster) Numeric vectors of sensitivity values.
delta_type: One of "eq" (equality, the default) or "bound".
r2long_type: One of "eq" (the default) or "relative". When "relative", values are multiplied by R-squared(medium).
maxovb_type: One of "bound" (default) or "relative". When "relative", values are multiplied by |Beta(medium)|.
beta: Hypothesis spec for the breakdown point. See regsen_breakdown().
product: Logical. If TRUE (default), all combinations of the sensitivity-parameter grids are evaluated; if FALSE, the inputs are zipped element-wise. Maps to Stata's noproduct option (inverted).
ngrid: Resolution of the finer grid stored in the result. Default 200.
subset: Optional logical or integer vector indicating which rows of data to include in the estimation.

Value

A regsensitivity object. The results field holds a data.frame with one row per sensitivity-parameter point.

For a breakdown analysis, results$breakdown is signed: its sign carries the direction of selection, and for Oster it is the delta that solves Proposition 3 for the hypothesised value. Feeding that value back into regsen_bounds() recovers the hypothesised beta, but feeding abs() of it lands on a different branch of the cubic. The scalar $breakdown field and the print method report the magnitude, since that is what is quoted as "the breakdown point". Note that the scalar exists on regsen_bounds() output only; a regsen_breakdown() result carries the value in results$breakdown alone.

Examples

# \donttest{
data(bfg2020)
bnds <- regsen_bounds(
  avgrep2000to2016 ~ tye_tfe890_500kNI_100_l6 +
    log_area_2010 + lat + lon + temp_mean + rain_mean + elev_mean +
    d_coa + d_riv + d_lak + ave_gyi,
  data = bfg2020,
  cbar = 0.1
)
print(bnds)
#> 
#> Regression Sensitivity Analysis ----- Bounds
#> ------------------------------------------------------------------------
#> Analysis:          DMP (2026)
#> Treatment:         tye_tfe890_500kNI_100_l6
#> Outcome:           avgrep2000to2016
#> N (obs):           2036
#> Hypothesis:        Beta > 0
#> Breakdown point:   0.3726
#> 
#> --- Summary statistics ----------------------------------
#>   Beta (short)                  1.7078
#>   Beta (medium)                 1.5864
#>   R2 (short)                    0.0269
#>   R2 (medium)                   0.1345
#>   Var(Y)                      136.3204
#>   Var(X)                        1.2574
#>   Var(X_Residual)               1.0903
#> 
#> --- Results ---------------------------------------------
#>    rxbar rybar   cbar     bmin   bmax
#>        0  +Inf    0.1   1.5864 1.5864
#>  0.22448  +Inf    0.1  0.65214 2.5207
#>  0.44897  +Inf    0.1 -0.35117  3.524
#>  0.67345  +Inf    0.1  -1.4627 4.6356
#>  0.89793  +Inf    0.1  -2.7437 5.9165
#>   1.1224  +Inf    0.1  -4.3004 7.4733
#>   1.3469  +Inf    0.1  -6.3455 9.5184
#>   1.5714  +Inf    0.1  -9.4032 12.576
#>   1.7959  +Inf    0.1  -15.393 18.566
#>   2.0204  +Inf    0.1  -60.525 63.698
#>   2.2448  +Inf    0.1     -Inf   +Inf
# }